Bond Prices vs. Interest Rates

Introduction

• Explanation of the inverse relationship between bond prices and interest rates.

Understanding Bonds

• Example bond details:
  • Issuer: Company A (could also be a municipality or government)
  • Face value: $1,000
  • Maturity: 2 years
  • Coupon: 10% paid semi-annually

Payment Schedule

• Timeline of payments:
  • Today (Day 0)
  • 6 months: $50 (first coupon payment)
  • 12 months: $50 (second coupon payment)
  • 18 months: $50 (third coupon payment)
  • 24 months: $1,000 (face value) + $50 (fourth coupon payment)

Pricing the Bond Initially

• Willingness to pay: $1,000 (price equals face value at issuance, 10% coupon is attractive)

Impact of Interest Rate Changes

Scenario 1: Interest Rates Increase

• Interest rates rise to 15%:
  • The bond only pays 10%, thus price decreases below $1,000.
  • Bond trades at a discount to par.

Scenario 2: Interest Rates Decrease

• Interest rates drop to 5%:
  • The bond pays 10%, making it more attractive.
  • Price increases above $1,000.
  • Bond trades at a premium to par.

Mathematical Pricing of Bonds

Zero-Coupon Bond Example

• Definition: A bond that pays only face value at maturity.
  • Face value: $1,000 in 2 years.

Calculating Present Value at 10% Interest Rate

• Formula: P = 1000 / (1 + 10%)^2
• Calculation:
  • P = $1,000 / 1.1^2 = $826

New Interest Rate Scenario: 15%

• New calculation:
• Price at 15%:
  • P = $1,000 / (1 + 15%)^2 = $756

New Interest Rate Scenario: 5%

• Price at 5%:
  • P = $1,000 / (1 + 5%)^2 = $907

Conclusion

• Summary of findings:
  • Price decreases when interest rates rise.
  • Price increases when interest rates fall.
• Key takeaway: Higher expected returns lead to lower bond prices.